Find the values of x such that the function $\displaystyle f^{2}$ maps onto $\displaystyle g$.

So we need to solve the equation $\displaystyle f^{2}(x)=g(x)$.

My students asked me why is that the equation to be solved. They don't understand about the "maps onto" part.

How should I explain this? a simple and straightforward explanation?

Thanks for sharing